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Naman Academy For Class 9
Chapter 13: Two Variables, One LineAll 3 Questions on This Page

Class 9 Maths Chapter 13 Exercise Set 13.4 Solutions

Step-by-step solutions for Class 9 Mathematics Ganita Manjari Part 1I Chapter 13 Exercise Set 13.4 (Questions 1–3). Covers framing pairs of linear equations in two variables from everyday situations, including movie tickets and snack purchases, taxi fares with fixed and per-kilometre charges, and sports meet ticket collections.

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Key Concepts for Exercise Set 13.4

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1

Framing Linear Equations from Everyday Situations

To model a practical situation with a linear equation, identify the two independent unknown quantities, assign distinct variables (such as x and y), and express the stated conditions algebraically as relations between those variables.

Identify unknown quantities ⇒ Assign variables (x, y) ⇒ Set up equations
2

Modeling Fixed and Variable (Rate-Based) Charges

Situations involving service charges, taxi fares, or rentals typically feature a fixed base charge plus an additional rate proportional to distance or quantity: Total Cost = Fixed Charge + (Rate per unit × Units).

Total fare = Fixed charge + (Distance × Charge per km) = x + dy
3

Quantity Totals vs. Value Totals

When dealing with different categories of items (such as adult and children tickets), one linear equation models the total number of items, while the second linear equation models the total monetary value collected.

Total count: x + y = N | Total value: p₁x + p₂y = Total Amount
Question 1
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On two different days a family buys movie tickets and snack boxes. Let the cost of one movie ticket be ₹x and the cost of one snack box be ₹y. Frame a pair of linear equations in x and y to represent the following situations: (i) On the first day, the family buys 2 movie tickets and 3 snack boxes for ₹850. (ii) On the second day, the family buys 4 movie tickets and 1 snack box for ₹1100.

Solution

Let the cost of one movie ticket be ₹x, and the cost of one snack box be ₹y.

(i) First day

The cost of 2 movie tickets is ₹2x.

The cost of 3 snack boxes is ₹3y.

The total cost is ₹850. Therefore,

2x + 3y = 850
(ii) Second day

The cost of 4 movie tickets is ₹4x.

The cost of 1 snack box is ₹y.

The total cost is ₹1100. Therefore,

4x + y = 1100
Answer:2x + 3y = 850, 4x + y = 1100
Question 2
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Two friends, Sahil and Meena, travelled by taxi. Let the fixed charge for one taxi trip be ₹x and the additional charge per kilometre be ₹y. Frame a pair of linear equations in x and y to represent the following situation: (i) Sahil travelled 6 km and paid a total fare of ₹122. (ii) Meena travelled 8 km and paid a total fare of ₹160.

Solution

Let the fixed charge for one taxi trip be ₹x, and the additional charge per kilometre be ₹y.

The total taxi fare is calculated as:

Total fare = Fixed charge + (Distance × Charge per km)
(i) Sahil travelled 6 km and paid ₹122

The additional charge for 6 km is ₹6y.

Therefore,
x + 6y = 122
(ii) Meena travelled 8 km and paid ₹160

The additional charge for 8 km is ₹8y.

Therefore,
x + 8y = 160
Answer:x + 6y = 122, x + 8y = 160
Question 3
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In a sports meet, tickets for adults cost ₹150 each and tickets for children cost ₹100 each. A total of 200 people attended the meet, and the total amount collected from ticket sales was ₹25,000. (Let the number of adult tickets sold be x and the number of children’s tickets sold be y.) Frame a pair of linear equations in x and y to represent this situation.

Solution

Let the number of adult tickets sold be x, and the number of children's tickets sold be y.

Equation 1: Total number of people

The number of adult tickets plus the number of children's tickets is 200.

Therefore,
x + y = 200
Equation 2: Total ticket collection

The cost of x adult tickets is ₹150x.

The cost of y children's tickets is ₹100y.

The total amount collected is ₹25,000. Therefore,

150x + 100y = 25000
Answer:x + y = 200, 150x + 100y = 25000

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